The F-gauge used in Friedrich's representation of spatial infinity is
a gauge prescription based on the properties of conformal geodesics
—i.e. a pair consisting of a curve and a covector along the curve
satisfying conformally invariant properties. A remarkable property of
conformal geodesics is that in Einstein spaces, they give rise to a
canonical factor that has a quadratic dependence on the parameter of
the curve —see [1]}, [2]}. The resulting expression
depends on certain initial data which can be chosen in such a way that
the curves reach the conformal boundary and that no caustics are
formed. In this way, one can obtain a conformal Gaussian gauge in which
coordinates and a frame defined on an initial hypersurface are
propagated along the conformal. In effect, this procedure provides a
canonical way of obtaining conformal extensions of Einstein
spaces. In the context of initial value problem for the conformal
Einstein equations, one has a gauge in which the location of the
conformal boundary is known a priori.
